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Oct 25, 2014
10/14
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St Onge, Joye; Ioannidis, George; Papaioannou, Alexandra; McLeod, Heather; Marr, Sharon
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This article is from BMC Medical Education , volume 13 . Abstract Background: The impact of geriatric medicine educational programs on patient level outcomes, as opposed to educational measures, is not well studied. We aimed to determine whether completion of a mandatory geriatrics rotation changed the clinical behaviors of clerks caring for older patients admitted to a medical clinical teaching unit. Methods: We reviewed the charts of 132 older (>70y) patients, admitted to one medical...
Source: http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3907134
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Sep 22, 2013
09/13
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George A. Hagedorn; Alain Joye
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Optimal truncations of asymptotic expansions are known to yield approximations to adiabatic quantum evolutions that are accurate up to exponentially small errors. In this paper, we rigorously determine the leading order non--adiabatic corrections to these approximations for a particular family of two--level analytic Hamiltonian functions. Our results capture the time development of the exponentially small transition that takes place between optimal states by means of a particular switching...
Source: http://arxiv.org/abs/math-ph/0309012v1
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Sep 18, 2013
09/13
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George A. Hagedorn; Alain Joye
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We present the construction of an exponentially accurate time-dependent Born-Oppenheimer approximation for molecular quantum mechanics. We study molecular systems whose electron masses are held fixed and whose nuclear masses are proportional to $\epsilon^{-4}$, where $\epsilon$ is a small expansion parameter. By optimal truncation of an asymptotic expansion, we construct approximate solutions to the time-dependent Schr\"odinger equation that agree with exact normalized solutions up to...
Source: http://arxiv.org/abs/math-ph/0005006v1
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Sep 22, 2013
09/13
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George A. Hagedorn; Alain Joye
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We propose an alternative to the usual time--independent Born--Oppenheimer approximation that is specifically designed to describe molecules with non--symmetrical hydrogen bonds. In our approach, the masses of the hydrogen nuclei are scaled differently from those of the heavier nuclei, and we employ a specialized form for the electron energy level surface. As a result, the different vibrational modes appear at different orders of approximation. Although we develop a general theory, our analysis...
Source: http://arxiv.org/abs/0805.4526v1
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Sep 20, 2013
09/13
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George A. Hagedorn; Alain Joye
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We propose an alternative to the usual time--independent Born--Oppenheimer approximation that is specifically designed to describe molecules with symmetrical Hydrogen bonds. In our approach, the masses of the Hydrogen nuclei are scaled differently from those of the heavier nuclei, and we employ a specialized form for the electron energy level surface. Consequently, anharmonic effects play a role in the leading order calculations of vibrational levels. Although we develop a general theory, our...
Source: http://arxiv.org/abs/math-ph/0607056v1
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Sep 23, 2013
09/13
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George A. Hagedorn; Alain Joye
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We review mathematical results concerning exponentially small corrections to adiabatic approximations and Born--Oppenheimer approximations.
Source: http://arxiv.org/abs/math-ph/0511067v1
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Sep 17, 2013
09/13
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Vasile Gradinaru; George A. Hagedorn; Alain Joye
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We study the time behavior of wave functions involved in tunneling through a smooth potential barrier in one dimension in the semiclassical limit. We determine the leading order component of the wave function that tunnels. It is exponentially small in $1/\hbar$. For a wide variety of incoming wave packets, the leading order tunneling component is Gaussian for sufficiently small $\hbar$. We prove this for both the large time asymptotics and for moderately large values of the time variable.
Source: http://arxiv.org/abs/1003.3280v1
Topics: Tyndale, William, d. 1536, Bible
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Sep 19, 2013
09/13
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George A. Hagedorn; Alain Joye
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We construct approximate solutions to the time--dependent Schr\"odinger equation $i \hbar (\partial \psi)/(\partial t) = - (\hbar^2)/2 \Delta \psi + V \psi$ for small values of $\hbar$. If $V$ satisfies appropriate analyticity and growth hypotheses and $|t|\le T$, these solutions agree with exact solutions up to errors whose norms are bounded by $C \exp{-\gamma/\hbar}$, for some $C$ and $\gamma>0$. Under more restrictive hypotheses, we prove that for sufficiently small $T', |t|\le T'...
Source: http://arxiv.org/abs/math-ph/9812025v1
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Sep 19, 2013
09/13
by
George A. Hagedorn; Alain Joye
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We prove six theorems concerning exponentially accurate semiclassical quantum mechanics. Two of these theorems are known results, but have new proofs. Under appropriate hypotheses, they conclude that the exact and approximate dynamics of an initially localized wave packet agree up to exponentially small errors in $\hbar$ for finite times and for Ehrenfest times. Two other theorems state that for such times the wave packets are localized near a classical orbit up to exponentially small errors....
Source: http://arxiv.org/abs/math-ph/9911036v1
